检查给定矩阵是否为幻方
给定一个矩阵，检查它是否是魔方。魔方是从 1 到 n 2的不同元素的 anxn 矩阵，其中任何行、列或对角线的总和始终等于相同的数字。
例子：
Input : n = 3
2 7 6
9 5 1
4 3 8
Output : Magic matrix
Explanation:In matrix sum of each
row and each column and diagonals sum is
same = 15.
Input : n = 3
1 2 2
2 2 1
2 1 2
Output : Not a Magic Matrix
Explanation:In matrix sum of each
row and each column and diagonals sum is
not same. 1. 求素对角线和次对角线之和。
2. 计算每一行和每一列的总和。
3.如果素数对角线和次对角线和等于每行和每列的和，则它是魔术矩阵。
C++
// C++ program to check whether a given
// matrix is magic matrix or not
#include
# define my_sizeof(type) ((char *)(&type+1)-(char*)(&type))
using namespace std;
// Returns true if mat[][] is magic
// square, else returns false.
bool isMagicSquare(int mat[][3])
{
int n = my_sizeof(mat)/my_sizeof(mat[0]);
// calculate the sum of
// the prime diagonal
int i=0,j=0;
// sumd1 and sumd2 are the sum of the two diagonals
int sumd1 = 0, sumd2=0;
for (i = 0; i < n; i++)
{
// (i, i) is the diagonal from top-left -> bottom-right
// (i, n - i - 1) is the diagonal from top-right -> bottom-left
sumd1 += mat[i][i];
sumd2 += mat[i][n-1-i];
}
// if the two diagonal sums are unequal then it is not a magic square
if(sumd1!=sumd2)
return false;
// For sums of Rows
for (i = 0; i < n; i++) {
int rowSum = 0, colSum = 0;
for (j = 0; j < n; j++)
{
rowSum += mat[i][j];
colSum += mat[j][i];
}
if (rowSum != colSum || colSum != sumd1)
return false;
}
return true;
}
// driver program to
// test above function
int main()
{
int mat[3][3] = {{ 2, 7, 6 },
{ 9, 5, 1 },
{ 4, 3, 8 }};
if (isMagicSquare(mat))
cout << "Magic Square";
else
cout << "Not a magic Square";
return 0;
} Java
// JAVA program to check whether a given
// matrix is magic matrix or not
import java.io.*;
class GFG {
static int N = 3;
// Returns true if mat[][] is magic
// square, else returns false.
static boolean isMagicSquare(int mat[][])
{
// sumd1 and sumd2 are the sum of the two diagonals
int sumd1 = 0,sumd2=0;
for (int i = 0; i < N; i++)
{
// (i, i) is the diagonal from top-left -> bottom-right
// (i, N - i - 1) is the diagonal from top-right -> bottom-left
sumd1 += mat[i][i];
sumd2 += mat[i][N-1-i];
}
// if the two diagonal sums are unequal then it is not a magic square
if(sumd1!=sumd2)
return false;
// calculating sums of Rows and columns and checking if they are equal to each other,
// as well as equal to diagonal sum or not
for (int i = 0; i < N; i++) {
int rowSum = 0, colSum = 0;
for (int j = 0; j < N; j++)
{
rowSum += mat[i][j];
colSum += mat[j][i];
}
if (rowSum != colSum || colSum != sumd1)
return false;
}
return true;
}
// driver program to
// test above function
public static void main(String[] args)
{
int mat[][] = {{ 2, 7, 6 },
{ 9, 5, 1 },
{ 4, 3, 8 }};
if (isMagicSquare(mat))
System.out.println("Magic Square");
else
System.out.println("Not a magic" +
" Square");
}
}Python3
# Python3 program to check whether a given
# matrix is magic matrix or not
# Returns true if mat[][] is magic
# square, else returns false.
def isMagicSquare( mat) :
n = len(mat)
# sumd1 and sumd2 are the sum of the two diagonals
sumd1=0
sumd2=0
for i in range(n):
# (i, i) is the diagonal from top-left -> bottom-right
# (i, n - i - 1) is the diagonal from top-right -> bottom-left
sumd1+=mat[i][i]
sumd2+=mat[i][n-i-1]
# if the two diagonal sums are unequal then it is not a magic square
if not(sumd1==sumd2):
return False
for i in range(n):
#sumr is rowsum and sumc is colsum
sumr=0
sumc=0
for j in range(n):
sumr+=mat[i][j]
sumc+=mat[j][i]
if not(sumr==sumc==sumd1):
return False
#if all the conditions are satisfied then it is a magic square
return True
# Driver Code
mat = [ [ 2, 7, 6 ],
[ 9, 5, 1 ],
[ 4, 3, 8 ] ]
if (isMagicSquare(mat)) :
print( "Magic Square")
else :
print( "Not a magic Square")C#
// C# program to check whether a given
// matrix is magic matrix or not
using System;
class GFG
{
static int N = 3;
// Returns true if mat[][] is magic
// square, else returns false.
static bool isMagicSquare(int[,] mat)
{
// sumd1 and sumd2 are the sum of the two diagonals
int sumd1 = 0, sumd2 = 0;
for (int i = 0; i < N; i++)
{
// (i, i) is the diagonal from top-left -> bottom-right
// (i, N - i - 1) is the diagonal from top-right -> bottom-left
sumd1 = sumd1 + mat[i, i];
sumd2 = sumd2 + mat[i, N-1-i];
}
// if the two diagonal sums are unequal then it is not a magic square
if(sumd1!=sumd2)
return false;
// For sums of Rows
for (int i = 0; i < N; i++) {
int rowSum = 0, colSum = 0;
for (int j = 0; j < N; j++)
{
rowSum += mat[i, j];
colSum += mat[j,i];
}
if (rowSum != colSum || colSum != sumd1)
return false;
}
return true;
}
// Driver Code
public static void Main()
{
int[,] mat =new int [,] {{ 2, 7, 6 },
{ 9, 5, 1 },
{ 4, 3, 8 }};
if (isMagicSquare(mat))
Console.WriteLine("Magic Square");
else
Console.WriteLine("Not a magic" +
" Square");
}
}PHP
bottom-right
// (i, N - i - 1) is the diagonal from top-right -> bottom-left
$sumd1 = $sumd1 + $mat[$i][$i];
$sumd2 = $sumd2 + $mat[$i][$N-$i-1];
}
// if the two diagonal sums are unequal then it is not a magic square
if( $sumd1 != $sumd2)
return false;
for($i = 0; $i < $N; $i++)
{
$rowSum = 0; $colSum = 0;
for ($j = 0; $j < $N; $j++)
{
$rowSum += $mat[$i][$j];
$colSum += $mat[$j][$i];
}
if ($rowSum != $colSum || $colSum != $sumd1)
return false;
}
return true;
}
// Driver Code
{
$mat = array(array(2, 7, 6),
array(9, 5, 1),
array(4, 3, 8));
if (isMagicSquare($mat))
echo "Magic Square";
else
echo "Not a magic Square";
return 0;
}
?>Javascript
输出
Magic Square